**Sent:** Thursday, May 22, 2003 9:17
PM

**Subject:** [APBR_analysis] Re: Defensing
the Mavs

The other thing with bowen is sample size. he is a bad
free throw

shooter but he rarely goes to line (1.1 per game). In
the two years

that bowen shot over 100 free throws he shot about
61%. I suspect

the more you foul him the less it helps.

` I don't think so -- there doesn't seem to be much
of a pattern when you look at his FT% broken down by FTA in each
game:`

` FTA
games FT%`

1
16 37.5%

2
105 52.4%

3
11 48.5%

4
42 57.1%

5 5
64.0%

6
9 53.7%

7 3
47.6%

8
3 66.7%

9 1
66.7%

`ed`

[Michael Tamada] Actually those numbers do indicate a weak
positive relationship between Bowen's FTA and FT%. If we simply regress
the FT% on the FTA (so, just 9 observations), a linear regression suggests
that his FT% rises by 2.6 percentage points for each additional FTA he
attempts. This is significant at the p=2.9% level (adjusted R2 =
.45).

That
simple 9-observation regression of course is misleading because some of those
FTA/FT% combinations occured a lot more frequently than others. When we
treat each game as an observation (so 195 observations), we get a worse fit
(adjusted R2 = .39), and a smaller slope estimate (2.3 percentage point
increase in FT%), but with the larger number of observations the results
become highly statistically significant (p < 1%).

Pretty much the same results can be obtained by using
a simpler technique: really, the only combinations with large
numbers of observations are 2 FTA and 4 FTA. Bowen's FT% appears to rise
from 52.4% to 57.1% over that range, implying that each FTA raises his FT% by
2.35 percentage points.

If
we take the regression equation literally, then each additional FTA per game
raises Bowen's FT% by 2.3 percentage points -- implying that the marginal FTA
has a 4.6 high percentage point probability than the previous one. And
given his estimate y-intercept of .460, if Bowen ever attempts 11
FTs in a game, he'll have over a 100% probability of making his 12th FT!
;)

--MKT